Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 536 - 551

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 03/2017, Volume 84, Issue 3, pp. 233 - 248

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 06/2018, Volume 88, Issue 2, pp. 312 - 336

A long unichord in a graph is an edge that is the unique chord of some cycle of length at least 5. A graph is long unichord free if it does not contain any...

05C75 | χ‐bounded | amalgam | chords | 05C85 | 05C15 | χ-bounded | Computer Science | Discrete Mathematics

05C75 | χ‐bounded | amalgam | chords | 05C85 | 05C15 | χ-bounded | Computer Science | Discrete Mathematics

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 2008, Volume 98, Issue 1, pp. 173 - 225

A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002,...

Balanced skew partition | Berge graph | 2-Join | Decomposition | Detection | Perfect graph | Recognition | PERFECT GRAPHS | MATHEMATICS | detection | STAR-CUTSETS | ALGORITHM | recognition | decomposition | 2-join | perfect graph | balanced skew partition | HOLE-FREE GRAPHS | Algorithms | Mathematics - Combinatorics | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Balanced skew partition | Berge graph | 2-Join | Decomposition | Detection | Perfect graph | Recognition | PERFECT GRAPHS | MATHEMATICS | detection | STAR-CUTSETS | ALGORITHM | recognition | decomposition | 2-join | perfect graph | balanced skew partition | HOLE-FREE GRAPHS | Algorithms | Mathematics - Combinatorics | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 08/2019

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 11/2009, Volume 25, Issue 4, pp. 489 - 502

The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time O(n 4) whether three given vertices of a graph belong to an induced tree. Here, we...

05C75 | 05C85 | Mathematics | Engineering Design | Four-in-a-tree | Algorithm | Three-in-a-tree | Induced subgraph | Triangle-free graphs | 90C35 | Tree | Combinatorics | 68R10 | 05C05 | MATHEMATICS | Algorithms | Graphs | Computer Science | Discrete Mathematics

05C75 | 05C85 | Mathematics | Engineering Design | Four-in-a-tree | Algorithm | Three-in-a-tree | Induced subgraph | Triangle-free graphs | 90C35 | Tree | Combinatorics | 68R10 | 05C05 | MATHEMATICS | Algorithms | Graphs | Computer Science | Discrete Mathematics

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 07/2019

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2005, Volume 19, Issue 3, pp. 553 - 574

We consider the class A of graphs that contain no odd hole, no antihole of length at least 5, and no prism ( a graph consisting of two disjoint triangles with...

Perfectly contractile | Even pair | Perfect graph | Recognition algorithm | recognition algorithm | MATHEMATICS, APPLIED | perfectly contractile | even pair | perfect graph | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Perfectly contractile | Even pair | Perfect graph | Recognition algorithm | recognition algorithm | MATHEMATICS, APPLIED | perfectly contractile | even pair | perfect graph | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 536 - 551

Equistable graphs are graphs admitting positive weights on vertices such that a subset of vertices is a maximal stable set if and only if it is of total...

05C76 | conjecture | 05C22 | 05C50 | 05C69 | equistable graph; strongly equistable graph; general partition graph; line graph; graph complement | MATHEMATICS | strongly equistable graph | graph complement | general partition graph | PARTITION GRAPHS | line graph | equistable graph | Computer Science | Discrete Mathematics

05C76 | conjecture | 05C22 | 05C50 | 05C69 | equistable graph; strongly equistable graph; general partition graph; line graph; graph complement | MATHEMATICS | strongly equistable graph | graph complement | general partition graph | PARTITION GRAPHS | line graph | equistable graph | Computer Science | Discrete Mathematics

Journal Article

Algorithmica, ISSN 0178-4617, 02/2018, Volume 80, Issue 2, pp. 415 - 447

Journal Article

Algorithmica, ISSN 0178-4617, 3/2017, Volume 77, Issue 3, pp. 619 - 641

The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Turing-kernel | Mathematics of Computing | Computer Science | FPT algorithm | Theory of Computation | Bull-free graph | Stable set | Algorithm Analysis and Problem Complexity | Kernel | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Computer science | Cattle | Discrete Mathematics

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Turing-kernel | Mathematics of Computing | Computer Science | FPT algorithm | Theory of Computation | Bull-free graph | Stable set | Algorithm Analysis and Problem Complexity | Kernel | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Computer science | Cattle | Discrete Mathematics

Journal Article

Algorithmica, ISSN 0178-4617, 2/2018, Volume 80, Issue 2, pp. 415 - 447

An ISK4 in a graph G is an induced subgraph of G that is isomorphic to a subdivision of $$K_4$$ K4 (the complete graph on four vertices). A wheel is a graph...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Theory of Computation | Algorithm Analysis and Problem Complexity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | ALGORITHM | Discrete Mathematics

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Theory of Computation | Algorithm Analysis and Problem Complexity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | ALGORITHM | Discrete Mathematics

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 03/2017, Volume 84, Issue 3, pp. 233 - 248

We prove a decomposition theorem for the class of triangle‐free graphs that do not contain a subdivision of the complete graph on four vertices as an induced...

decompostion | 05C75 | induced subdivision of K4 | coloring | MATHEMATICS | Computer Science | Discrete Mathematics

decompostion | 05C75 | induced subdivision of K4 | coloring | MATHEMATICS | Computer Science | Discrete Mathematics

Journal Article

Journal of Combinatorial Theory. Series B, ISSN 0095-8956, 2018

Truemper configurations are four types of graphs (namely thetas, wheels, prisms and pyramids) that play an important role in the proof of several decomposition...

Structure theorem | 2-Join | Decomposition | Induced subgraph | Recognition algorithm | Clique cutset | Truemper configuration

Structure theorem | 2-Join | Decomposition | Induced subgraph | Recognition algorithm | Clique cutset | Truemper configuration

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 10/2019, Volume 92, Issue 2, pp. 67 - 95

We show that triangle‐free graphs that do not contain an induced subgraph isomorphic to a subdivision of K 4 are 3‐colorable. This proves a conjecture of...

induced subgraph | coloring

induced subgraph | coloring

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 08/2017, Volume 85, Issue 4, pp. 814 - 838

A graph G has maximal local edge‐connectivity k if the maximum number of edge‐disjoint paths between every pair of distinct vertices x and y is at most k. We...

local connectivity | coloring | vertex degree | minimally k‐connected | Brooks’ theorem | local edge‐connectivity | local edge-connectivity | minimally k-connected | MATHEMATICS | Brooks' theorem | Computer Science | Discrete Mathematics

local connectivity | coloring | vertex degree | minimally k‐connected | Brooks’ theorem | local edge‐connectivity | local edge-connectivity | minimally k-connected | MATHEMATICS | Brooks' theorem | Computer Science | Discrete Mathematics

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 01/2010, Volume 63, Issue 1, pp. 31 - 67

We give a structural description of the class 𝒞 of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that...

detection | Petersen graph | cycle with a unique chord | recognition | decomposition | coloring | Heawood graph | structure | Coloring | Decomposition | Cycle with a unique chord | Detection | Structure | Recognition | MATHEMATICS | UNIMODULAR MATRICES | ALGORITHMS | BERGE GRAPHS | Mathematics - Combinatorics | Computer Science | Discrete Mathematics

detection | Petersen graph | cycle with a unique chord | recognition | decomposition | coloring | Heawood graph | structure | Coloring | Decomposition | Cycle with a unique chord | Detection | Structure | Recognition | MATHEMATICS | UNIMODULAR MATRICES | ALGORITHMS | BERGE GRAPHS | Mathematics - Combinatorics | Computer Science | Discrete Mathematics

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2012, Volume 26, Issue 4, pp. 1510 - 1531

We recall several known results about minimally 2-connected graphs and show that they all follow from a decomposition theorem. Starting from an analogy with...

Connectivity | Propeller | Wheels | Induced subgraph | wheels | MATHEMATICS, APPLIED | connectivity | propeller | induced subgraph | THEOREM | ALGORITHMS

Connectivity | Propeller | Wheels | Induced subgraph | wheels | MATHEMATICS, APPLIED | connectivity | propeller | induced subgraph | THEOREM | ALGORITHMS

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2008, Volume 22, Issue 1, pp. 51 - 71

We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of...

Combinatorial algorithms | Perfect graphs | Maximum weight clique algorithm | Recognition algorithm | Star decomposition | recognition algorithm | MATHEMATICS, APPLIED | combinatorial algorithms | star decomposition | perfect graphs | maximum weight clique algorithm | FREE PERFECT GRAPHS | INDEPENDENT SETS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Combinatorial algorithms | Perfect graphs | Maximum weight clique algorithm | Recognition algorithm | Star decomposition | recognition algorithm | MATHEMATICS, APPLIED | combinatorial algorithms | star decomposition | perfect graphs | maximum weight clique algorithm | FREE PERFECT GRAPHS | INDEPENDENT SETS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Journal Article

09/2013

M. Chudnovsky, P. Seymour and N. Trotignon. Detecting an induced net subdivision. Journal of Combinatorial Theory, Series B, 103(5):630-641, 2013 A {\em net}...

Journal Article

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